Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.
Stability of infinite matrices has important applications to spline approximation, wavelets, Gabor time-frequency analysis, etc. In this paper, perturbation analysis for convolution dominated infinite matrices was studied by introducing an idea of lp-stability at infinity. For infinite matrices in the Gohberg-Baskakov-Sjostrand class, a practical criterion for the lp-stability at infinity of convolution dominated infinite matrices on Zd under perturbation of compact operators was given.
